Question

以下四圖，都是同一坐標(biāo)系中三次函數(shù)及其導(dǎo)函數(shù)的圖像，其中一定的序號(hào)是

A．①、②

B．③、④

C．①、③

D．①、④

Answer 1

B

解析因?yàn)楫?dāng)原函數(shù)為增函數(shù)時(shí)，導(dǎo)數(shù)大于0，原函數(shù)為減函數(shù)時(shí)，導(dǎo)數(shù)小于0，原函數(shù)取得極值時(shí)，導(dǎo)數(shù)等于0，所以只需逐一判斷每個(gè)選項(xiàng)當(dāng)原函數(shù)是增或減時(shí)，導(dǎo)數(shù)的正負(fù)，就可找到正確選項(xiàng)．
解：①中三次函數(shù)的圖象由左到右是先減后增再減，對(duì)應(yīng)的導(dǎo)數(shù)是先小于0，，再大于0，最后又小于0，導(dǎo)數(shù)的正負(fù)與原函數(shù)的單調(diào)性一致，∴①正確．
②中三次函數(shù)的圖象由左到右是先減后增再減，對(duì)應(yīng)的導(dǎo)數(shù)是先小于0，再大于0，最后又小于0，導(dǎo)數(shù)的正負(fù)與原函數(shù)的單調(diào)性一致，∴②正確．
③中三次函數(shù)的圖象由左到右是先增后減再增，對(duì)應(yīng)的導(dǎo)數(shù)在原函數(shù)的增區(qū)間上既有負(fù)值，又有正值，導(dǎo)數(shù)的正負(fù)與原函數(shù)的單調(diào)性不一致，∴③錯(cuò)誤．
④中三次函數(shù)的圖象由左到右是先增后減再增，對(duì)應(yīng)的導(dǎo)數(shù)在原函數(shù)的增區(qū)間上為負(fù)值，導(dǎo)數(shù)的正負(fù)與原函數(shù)的單調(diào)性不一致，∴④錯(cuò)誤．
故選B